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受欢迎的三角函数 >

(30)/(sin(x))=(50)/(sin(90))

解答

\frac{30}{sin ( x )} = \frac{50}{sin ( 9 0 ^{\circ} )}

解答

x = 0.64350 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.64350 \dots + 36 0^{\circ} n

+1

弧度

x = 0.64350 \dots + 2 πn, x = π - 0.64350 \dots + 2 πn

求解步骤

\frac{30}{sin ( x )} = \frac{50}{sin ( 9 0 ^{\circ} )}

sin (9 0^{\circ}) = 1

sin (9 0^{\circ})

使用以下普通恒等式:

sin (9 0^{\circ}) = 1

sin (9 0^{\circ})

sin (x)

周期表（周期为

36 0^{\circ} n

"）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= 1

\frac{30}{sin ( x )} = \frac{50}{1}

使用分式交叉相乘

\frac{30}{sin ( x )} = \frac{50}{1}

使用分式交叉相乘: 若

\frac{a}{b} = \frac{c}{d}

则

a \cdot d = b \cdot c

30 \cdot 1 = sin (x) \cdot 50

化简

30 \cdot 1 : 30

30 \cdot 1

数字相乘:

30 \cdot 1 = 30

= 30

30 = sin (x) \cdot 50

30 = sin (x) \cdot 50

交换两边

sin (x) \cdot 50 = 30

两边除以

50

sin (x) \cdot 50 = 30

两边除以

50

\frac{sin ( x ) \cdot 50}{50} = \frac{30}{50}

化简

sin (x) = \frac{3}{5}

sin (x) = \frac{3}{5}

验证解

找到无定义的点（奇点）:

sin (x) = 0

取

\frac{30}{sin ( x )}

的分母，令其等于零

sin (x) = 0

以下点无定义

sin (x) = 0

将不在定义域的点与解相综合:

sin (x) = \frac{3}{5}

使用反三角函数性质

sin (x) = \frac{3}{5}

sin (x) = \frac{3}{5}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x = arcsin (\frac{3}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3}{5}) + 36 0^{\circ} n

x = arcsin (\frac{3}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3}{5}) + 36 0^{\circ} n

以小数形式表示解

x = 0.64350 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.64350 \dots + 36 0^{\circ} n

作图

流行的例子

cos(θ)=(2sqrt(3))/5

cos (θ) = \frac{2 3}{5}

cos(2x)(sin(x)+(sqrt(2))/2)=0

cos (2 x) (sin (x) + \frac{2}{2}) = 0

5 sin (θ) = 5

2sin(3x)=2,0<= x<= 2pi

2 sin (3 x) = 2, 0 \leq x \leq 2 π

1 - tan (x) = 0